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   MRCLASS = {14E07 (14L30)},
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MRREVIEWER = {I. Dolgachev},
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   MRCLASS = {26.00},
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}

@article {Arnold1957,
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}

@incollection {Dixmier1993Hilbert,
    AUTHOR = {Dixmier, Jacques},
     TITLE = {Histoire du 13e probl\`eme de {H}ilbert},
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    SERIES = {Cahiers S\'em. Hist. Math. S\'er. 2},
    VOLUME = {3},
     PAGES = {85--94},
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MRREVIEWER = {Chr. U. Jensen},
}

@misc {ColKunPopZin2009Is_the_function,
	Author = {Jean-Louis Colliot-Th{\'e}l{\`e}ne and Boris Kunyavski{\u \i} and Vladimir L. Popov and Zinovy Reichstein},
	Title = {Is the function field of a reductive Lie algebra purely transcendental over the field of invariants for the adjoint action?},
	Year = {2009},
	NOTE = {arXiv:0901.4358v5 [math.AG]}
}

@misc {Beauville2011On_finite_simpl,
	AUTHOR = {Beauville, Arnaud},
	TITLE = {On finite simple groups of essential dimension 3},
	YEAR = {2011},
	NOTE = {arXiv:1101.1372v2 [math.AG]}
}

@misc {DuncanED2v1,
	AUTHOR = {Duncan, Alexander},
	TITLE = {Finite Groups of Essential Dimension 2},
	YEAR = {2009},
	NOTE = {arXiv:0912.1644v1 [math.AG]}
}

@misc {DuncanED2v2,
	AUTHOR = {Duncan, Alexander},
	TITLE = {Finite Groups of Essential Dimension 2},
	Journal = {Commentarii Mathematici Helvetici},
	YEAR = {2010},
	NOTE = {To Appear.}
}

@article{DuncanEDS7,
	Author = {Alexander Duncan},
	Title = {Essential Dimensions of {$A_7$} and {$S_7$}},
	Journal = {Math. Res. Lett.},
	Volume = {17},
	Number = {2},
	Pages = {263-266},
	Year = {2010}
}

%%%%%%%

@book {Serre2002Galois_cohomolo,
AUTHOR = {Serre, Jean-Pierre},
TITLE = {Galois cohomology},
SERIES = {Springer Monographs in Mathematics},
EDITION = {English},
NOTE = {Translated from the French by Patrick Ion and revised by the author},
PUBLISHER = {Springer-Verlag},
ADDRESS = {Berlin},
YEAR = {2002},
PAGES = {x+210},
ISBN = {3-540-42192-0},
MRCLASS = {12G05 (11R34)},
MRNUMBER = {1867431 (2002i:12004)}
}}




%%%%%%%

@unpublished{Kan2006EDFG,
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	Note = "arXiv:math/0611673v2 [math.AG]",
	Title = {Essential dimensions of finite groups},
	Year = {2006}}

@book {ConCurNorPar1985AFG,
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 PUBLISHER = {Oxford University Press},
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      YEAR = {1985},
     PAGES = {xxxiv+252},
      ISBN = {0-19-853199-0}
}

%%%%%%%%%%%%%%%

@article {Saltman1982Generic_Galois_,
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@article {DeMeyer1983Generic_polynom,
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}

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@UNPUBLISHED{CoxLittleSchenckToric_Varieties,
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	Title = {Toric Varieties},
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	MONTH = {June}
}


@incollection {CoxKrasauskasMustata2003Universal_ratio,
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    AUTHOR = {Steinberg, Robert},
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    NUMBER = {25},
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   MRCLASS = {14.50 (20.75)},
  MRNUMBER = {MR0180554 (31 \#4788)},
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}

@article {Hosoh1997Automorphism-grou,
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@unpublished{SerreReichstein2005Essential-Dimen,
	Author = {Serre, Jean-Pierre and Reichstein, Zinovy},
	Date-Added = {2008-10-26 13:03:46 -0700},
	Date-Modified = {2008-10-26 13:05:52 -0700},
	Month = {May},
	Note = {Personal Correspondence},
	Title = {Essential Dimension Correspondence},
	Year = {2005},
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@article{Serre2008Le-group-de-cre,
	Author = {Serre, Jean-Pierre},
	Date-Added = {2008-10-26 13:02:12 -0700},
	Date-Modified = {2008-10-26 13:03:35 -0700},
	Journal = {S\'eminaire Bourbaki},
	Title = {Le groupe de {C}remona et ses sous-groupes finis},
	Year = {2008},
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@book{MillerBlichfeldtDickson1961Theory-and-appl,
	Address = {New York},
	Author = {Miller, G. A. and Blichfeldt, H. F. and Dickson, L. E.},
	Date-Added = {2008-10-26 12:59:30 -0700},
	Date-Modified = {2008-10-26 12:59:31 -0700},
	Mrclass = {20.25},
	Mrnumber = {MR0123600 (23 \#A925)},
	Pages = {xvii+390},
	Publisher = {Dover Publications Inc.},
	Title = {Theory and applications of finite groups},
	Year = {1961},
	Bdsk-File-1 = {YnBsaXN0MDDUAQIDBAUGCQpYJHZlcnNpb25UJHRvcFkkYXJjaGl2ZXJYJG9iamVjdHMSAAGGoNE
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@incollection{Fantechi2001Stacks-for-ever,
	Address = {Basel},
	Author = {Fantechi, Barbara},
	Booktitle = {European {C}ongress of {M}athematics, {V}ol. {I} ({B}arcelona,               2000)},
	Date-Added = {2008-10-26 12:56:41 -0700},
	Date-Modified = {2008-10-26 12:56:43 -0700},
	Mrclass = {14A20},
	Mrnumber = {MR1905329 (2003h:14003)},
	Mrreviewer = {Gabriele Vezzosi},
	Pages = {349--359},
	Publisher = {Birkh\"auser},
	Series = {Progr. Math.},
	Title = {Stacks for everybody},
	Volume = {201},
	Year = {2001},
	Bdsk-File-1 = {YnBsaXN0MDDUAQIDBAUGCQpYJHZlcnNpb25UJHRvcFkkYXJjaGl2ZXJYJG9iamVjdHMSAAGGoNE
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@article{LemirePopovReichstein2006Cayley-groups,
	Author = {Lemire, Nicole and Popov, Vladimir L. and Reichstein, Zinovy},
	Date-Added = {2008-10-26 12:55:19 -0700},
	Date-Modified = {2008-10-26 12:55:21 -0700},
	Fjournal = {Journal of the American Mathematical Society},
	Issn = {0894-0347},
	Journal = {J. Amer. Math. Soc.},
	Mrclass = {14L35 (14L40 17B45 20C10)},
	Mrnumber = {MR2219306 (2007e:14074)},
	Mrreviewer = {Dmitrii A. Timash{\"e}v},
	Number = {4},
	Pages = {921--967 (electronic)},
	Title = {Cayley groups},
	Volume = {19},
	Year = {2006},
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@article{Dress1975The-permutation,
	Author = {Dress, Andreas W. M.},
	Date-Added = {2008-10-15 16:34:07 -0700},
	Date-Modified = {2008-10-15 16:34:40 -0700},
	Fjournal = {Journal of Pure and Applied Algebra},
	Issn = {0022-4049},
	Journal = {J. Pure Appl. Algebra},
	Mrclass = {20C05},
	Mrnumber = {MR0360773 (50 \#13220)},
	Mrreviewer = {A. O. Morris},
	Pages = {1--12},
	Title = {The permutation class group of a finite group},
	Volume = {6},
	Year = {1975},
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@article{HanakiHida1992A-remark-on-Msb,
	Author = {Hanaki, Akihide and Hida, Akihiko},
	Coden = {OJMAA7},
	Date-Added = {2008-10-10 18:14:45 -0700},
	Date-Modified = {2008-10-10 18:14:46 -0700},
	Fjournal = {Osaka Journal of Mathematics},
	Issn = {0030-6126},
	Journal = {Osaka J. Math.},
	Mrclass = {20C20 (20C15)},
	Mrnumber = {MR1153180 (93c:20020)},
	Mrreviewer = {I. M. Isaacs},
	Number = {1},
	Pages = {71--74},
	Title = {A remark on {$M\sb p$}-groups},
	Volume = {29},
	Year = {1992},
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@article{StillmanTestaVelasco2007Grobner-bases-m,
	Author = {Stillman, Mike and Testa, Damiano and Velasco, Mauricio},
	Coden = {JALGA4},
	Date-Added = {2008-10-10 18:13:51 -0700},
	Date-Modified = {2008-10-10 18:13:53 -0700},
	Fjournal = {Journal of Algebra},
	Issn = {0021-8693},
	Journal = {J. Algebra},
	Mrclass = {14J26 (13P10)},
	Mrnumber = {MR2358614 (2008i:14054)},
	Mrreviewer = {C{\'{\i}}cero Carvalho},
	Number = {2},
	Pages = {777--801},
	Title = {Gr\"obner bases, monomial group actions, and the {C}ox rings               of del {P}ezzo surfaces},
	Volume = {316},
	Year = {2007},
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@misc{Reid2002Graded-rings-an,
	Author = {Reid, Miles},
	Date-Added = {2008-09-17 14:23:33 -0700},
	Date-Modified = {2008-09-17 14:24:09 -0700},
	Title = {Graded rings and varieties in weighted projective space},
	Year = {2002},
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@misc{BaezStay2008Physics-Topolog,
	Author = {Baez, John C. and Stay, Mike},
	Date-Added = {2008-09-17 14:22:16 -0700},
	Date-Modified = {2008-09-17 14:23:16 -0700},
	Title = {Physics, Topology, Logic and Computation: A Rosetta Stone},
	Year = {2008},
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@misc{Merkurjev2008Essential-dimen,
	Author = {Merkurjev, Alexander},
	Date-Added = {2008-09-17 14:20:44 -0700},
	Date-Modified = {2008-09-17 14:21:18 -0700},
	Title = {Essential dimension},
	Year = {2008},
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@misc{SerganovaSkorobogatovOn-the-equation,
	Author = {Vera Serganova and Alexei Skorobogatov},
	Date-Added = {2008-09-17 14:16:46 -0700},
	Date-Modified = {2008-09-17 14:20:20 -0700},
	Title = {On the equations for universal torsors over del {P}ezzo surfaces},
	Url = {http://arxiv.org/abs/0806.0089},
	Bdsk-File-1 = {YnBsaXN0MDDUAQIDBAUGCQpYJHZlcnNpb25UJHRvcFkkYXJjaGl2ZXJYJG9iamVjdHMSAAGGoNE
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@article{BarrWells2005Toposes-triples,
	Author = {Barr, Michael and Wells, Charles},
	Date-Added = {2008-09-17 14:15:09 -0700},
	Date-Modified = {2008-09-17 14:15:18 -0700},
	Fjournal = {Reprints in Theory and Applications of Categories},
	Issn = {1201-561X},
	Journal = {Repr. Theory Appl. Categ.},
	Mrclass = {18-02 (03G30 18B25 18C10 18C15)},
	Mrnumber = {MR2178101},
	Note = {Corrected reprint of the 1985 original [MR0771116]},
	Number = {12},
	Pages = {x+288 pp. (electronic)},
	Title = {Toposes, triples and theories},
	Year = {2005},
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@article{Lawvere2005Taking-categori,
	Author = {Lawvere, F. William},
	Date-Added = {2008-09-17 14:14:13 -0700},
	Date-Modified = {2008-09-17 14:14:15 -0700},
	Fjournal = {Reprints in Theory and Applications of Categories},
	Issn = {1201-561X},
	Journal = {Repr. Theory Appl. Categ.},
	Mrclass = {18D15 (00A30 37-XX 54E35)},
	Mrnumber = {MR2125316},
	Note = {Reprinted from Rev. Colombiana Mat. {{\bf{2}}0} (1986), no.               3-4, 147--178 [MR0948965]},
	Number = {8},
	Pages = {1--24 (electronic)},
	Title = {Taking categories seriously},
	Year = {2005},
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@incollection{GuralnickLorenz2006Orders-of-finit,
	Address = {Providence, RI},
	Author = {Guralnick, Robert M. and Lorenz, Martin},
	Booktitle = {Groups, rings and algebras},
	Date-Added = {2008-09-17 14:12:06 -0700},
	Date-Modified = {2008-09-17 14:12:24 -0700},
	Mrclass = {20C15 (20G40)},
	Mrnumber = {MR2279238 (2008e:20007)},
	Mrreviewer = {Shigeo Koshitani},
	Pages = {141--161},
	Publisher = {Amer. Math. Soc.},
	Series = {Contemp. Math.},
	Title = {Orders of finite groups of matrices},
	Volume = {420},
	Year = {2006},
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@article{Hausen2002Equivariant-emb,
	Author = {Hausen, J{\"u}rgen},
	Coden = {CJMAAB},
	Date-Added = {2008-09-17 14:11:20 -0700},
	Date-Modified = {2008-09-17 14:11:24 -0700},
	Fjournal = {Canadian Journal of Mathematics. Journal Canadien de               Math\'ematiques},
	Issn = {0008-414X},
	Journal = {Canad. J. Math.},
	Mrclass = {14M25 (14L24 14L30)},
	Mrnumber = {MR1900763 (2003c:14055)},
	Mrreviewer = {Dmitrii A. Timash{\"e}v},
	Number = {3},
	Pages = {554--570},
	Title = {Equivariant embeddings into smooth toric varieties},
	Volume = {54},
	Year = {2002},
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@webpage{BrunsGubeladzePolytopes-rings,
	Author = {Bruns, Winfried and Gubeladze, Joseph},
	Date-Added = {2008-09-17 14:06:01 -0700},
	Date-Modified = {2008-09-17 14:10:11 -0700},
	Title = {Polytopes, rings and {K}-theory},
	Url = {http://math.sfsu.edu/gubeladze/publications/kripo/kripo.pdf},
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@article{Ito1952Note-on-A-group,
	Author = {It{\^o}, Noboru},
	Date-Added = {2008-09-17 14:01:19 -0700},
	Date-Modified = {2008-09-17 14:01:25 -0700},
	Fjournal = {Nagoya Mathematical Journal},
	Issn = {0027-7630},
	Journal = {Nagoya Math. J.},
	Mrclass = {20.0X},
	Mrnumber = {MR0047656 (13,909c)},
	Mrreviewer = {J. Levitzki},
	Pages = {79--81},
	Title = {Note on {$A$}-groups},
	Volume = {4},
	Year = {1952},
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@article{Collins2008Bounds-for-fini,
	Author = {Collins, Michael J.},
	Coden = {JALGA4},
	Date-Added = {2008-09-17 13:59:59 -0700},
	Date-Modified = {2008-09-17 14:00:01 -0700},
	Fjournal = {Journal of Algebra},
	Issn = {0021-8693},
	Journal = {J. Algebra},
	Mrclass = {20Gxx},
	Mrnumber = {MR2381807},
	Number = {2},
	Pages = {759--776},
	Title = {Bounds for finite primitive complex linear groups},
	Volume = {319},
	Year = {2008},
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@article{Wild2005The-groups-of-o,
	Author = {Wild, Marcel},
	Coden = {AMMYAE},
	Date-Added = {2008-09-17 13:58:42 -0700},
	Date-Modified = {2008-09-17 13:58:43 -0700},
	Fjournal = {The American Mathematical Monthly},
	Issn = {0002-9890},
	Journal = {Amer. Math. Monthly},
	Mrclass = {20D99},
	Mrnumber = {MR2110109},
	Number = {1},
	Pages = {20--31},
	Title = {The groups of order sixteen made easy},
	Volume = {112},
	Year = {2005},
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@article{HochschildSerre1953Cohomology-of-g,
	Author = {Hochschild, G. and Serre, J.-P.},
	Date-Added = {2008-09-17 13:57:52 -0700},
	Date-Modified = {2008-09-17 13:57:54 -0700},
	Fjournal = {Transactions of the American Mathematical Society},
	Issn = {0002-9947},
	Journal = {Trans. Amer. Math. Soc.},
	Mrclass = {20.0X},
	Mrnumber = {MR0052438 (14,619b)},
	Mrreviewer = {H. Cartan},
	Pages = {110--134},
	Title = {Cohomology of group extensions},
	Volume = {74},
	Year = {1953},
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@article{Griess1991Elementary-abel,
	Author = {Griess, Jr., Robert L.},
	Coden = {GEMDAT},
	Date-Added = {2008-09-17 13:56:44 -0700},
	Date-Modified = {2008-09-17 13:56:46 -0700},
	Fjournal = {Geometriae Dedicata},
	Issn = {0046-5755},
	Journal = {Geom. Dedicata},
	Mrclass = {20G15},
	Mrnumber = {MR1123145 (92i:20047)},
	Mrreviewer = {Martin W. Liebeck},
	Number = {3},
	Pages = {253--305},
	Title = {Elementary abelian {$p$}-subgroups of algebraic groups},
	Volume = {39},
	Year = {1991},
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@article{Colliot-TheleneSansuc1987Principal-homog,
	Author = {Colliot-Th{\'e}l{\`e}ne, Jean-Louis and Sansuc, Jean-Jacques},
	Coden = {JALGA4},
	Date-Added = {2008-09-17 13:55:31 -0700},
	Date-Modified = {2008-09-17 13:55:33 -0700},
	Fjournal = {Journal of Algebra},
	Issn = {0021-8693},
	Journal = {J. Algebra},
	Mrclass = {14L40 (11E04 11E81 11G99 12E15 12F99 14D25 16A39)},
	Mrnumber = {MR878473 (88j:14059)},
	Mrreviewer = {David J. Saltman},
	Number = {1},
	Pages = {148--205},
	Title = {Principal homogeneous spaces under flasque tori: applications},
	Volume = {106},
	Year = {1987},
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@article{ACampo-NeuenHausen1999Quotients-of-to,
	Author = {A'Campo-Neuen, Annette and Hausen, J{\"u}rgen},
	Coden = {TOMJAM},
	Date-Added = {2008-09-17 13:54:10 -0700},
	Date-Modified = {2008-09-17 13:54:14 -0700},
	Fjournal = {The Tohoku Mathematical Journal. Second Series},
	Issn = {0040-8735},
	Journal = {Tohoku Math. J. (2)},
	Mrclass = {14L30 (14M25)},
	Mrnumber = {MR1671722 (99m:14088)},
	Mrreviewer = {Dmitrii A. Timash{\"e}v},
	Number = {1},
	Pages = {1--12},
	Title = {Quotients of toric varieties by the action of a subtorus},
	Volume = {51},
	Year = {1999},
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@article{KraftSchwarz1992Reductive-group,
	Author = {Kraft, Hanspeter and Schwarz, Gerald W.},
	Coden = {PMIHA6},
	Date-Added = {2008-09-17 13:52:09 -0700},
	Date-Modified = {2008-09-17 13:53:09 -0700},
	Fjournal = {Institut des Hautes \'Etudes Scientifiques. Publications               Math\'ematiques},
	Issn = {0073-8301},
	Journal = {Inst. Hautes \'Etudes Sci. Publ. Math.},
	Mrclass = {14L30 (14D20)},
	Mrnumber = {MR1215592 (94e:14065)},
	Mrreviewer = {V. L. Popov},
	Number = {76},
	Pages = {1--97},
	Title = {Reductive group actions with one-dimensional quotient},
	Year = {1992},
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@misc{Dolgachev2008Topics-in-Class,
	Author = {Dolgachev, Igor V.},
	Date-Added = {2008-09-01 16:09:57 -0700},
	Date-Modified = {2008-09-01 16:10:33 -0700},
	Title = {Topics in Classical Algebraic Geometry},
	Year = {2008},
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@article{KunyavskiuiSkorobogatovTsfasman1989del-Pezzo-surfa,
	Author = {Kunyavski{\u\i}, B. {\`E}. and Skorobogatov, A. N. and               Tsfasman, M. A.},
	Date-Added = {2008-08-18 18:32:05 -0700},
	Date-Modified = {2008-08-18 18:32:10 -0700},
	Fjournal = {M\'emoires de la Soci\'et\'e Math\'ematique de France.               Nouvelle S\'erie},
	Issn = {0037-9484},
	Journal = {M\'em. Soc. Math. France (N.S.)},
	Mrclass = {14J26},
	Mrnumber = {MR1016354 (90k:14035)},
	Mrreviewer = {Noriko Yui},
	Number = {37},
	Pages = {113},
	Title = {del {P}ezzo surfaces of degree four},
	Year = {1989},
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@article {Manin1967Rational-surfac,
    AUTHOR = {Manin, Yuri I.},
     TITLE = {Rational surfaces over perfect fields. {II}},
   JOURNAL = {Mat. Sb. (N.S.)},
    VOLUME = {72 (114)},
      YEAR = {1967},
     PAGES = {161--192},
   MRCLASS = {14.20},
  MRNUMBER = {MR0225781 (37 \#1374)},
MRREVIEWER = {M. L. Laplaza},
}

@book{Manin1986Cubic-forms,
	Address = {Amsterdam},
	Author = {Manin, Yuri I.},
	Date-Added = {2008-08-10 17:37:23 -0700},
	Date-Modified = {2008-08-10 17:37:24 -0700},
	Edition = {Second},
	Isbn = {0-444-87823-8},
	Mrclass = {11Gxx (14Gxx 14J20)},
	Mrnumber = {MR833513 (87d:11037)},
	Note = {Algebra, geometry, arithmetic,               Translated from the Russian by M. Hazewinkel},
	Pages = {x+326},
	Publisher = {North-Holland Publishing Co.},
	Series = {North-Holland Mathematical Library},
	Title = {Cubic forms},
	Volume = {4},
	Year = {1986}}

@book{GaribaldiMerkurjevSerre2003Cohomological-i,
	Address = {Providence, RI},
	Author = {Garibaldi, Skip and Merkurjev, Alexander and Serre,               Jean-Pierre},
	Date-Added = {2008-08-10 14:15:00 -0700},
	Date-Modified = {2008-08-10 14:15:01 -0700},
	Isbn = {0-8218-3287-5},
	Mrclass = {11E72 (12G05)},
	Mrnumber = {MR1999383 (2004f:11034)},
	Mrreviewer = {Gr{\'e}gory Berhuy},
	Pages = {viii+168},
	Publisher = {American Mathematical Society},
	Series = {University Lecture Series},
	Title = {Cohomological invariants in {G}alois cohomology},
	Volume = {28},
	Year = {2003}}

@book{Hartshorne1977Algebraic-geome,
	Address = {New York},
	Author = {Hartshorne, Robin},
	Date-Added = {2008-08-10 14:11:35 -0700},
	Date-Modified = {2008-08-10 14:11:38 -0700},
	Isbn = {0-387-90244-9},
	Mrclass = {14-01},
	Mrnumber = {MR0463157 (57 \#3116)},
	Mrreviewer = {Robert Speiser},
	Note = {Graduate Texts in Mathematics, No. 52},
	Pages = {xvi+496},
	Publisher = {Springer-Verlag},
	Title = {Algebraic geometry},
	Year = {1977}}

@misc{Reichstein2008Essential-dimen,
	Author = {Reichstein, Zinovy},
	Date-Added = {2008-08-10 13:40:04 -0700},
	Date-Modified = {2008-08-10 13:41:15 -0700},
	Title = {Essential dimension: a survey},
	Url = {http://www.math.ubc.ca/~reichst/lens-notes6-27-8.pdf},
	Year = {2008},
	Bdsk-Url-1 = {http://www.math.ubc.ca/~reichst/lens-notes6-27-8.pdf}}

@article{BerhuyFavi2003Essential-dimen,
	Author = {Berhuy, Gr{\'e}gory and Favi, Giordano},
	Date-Added = {2008-08-10 13:21:54 -0700},
	Date-Modified = {2008-08-10 13:22:00 -0700},
	Fjournal = {Documenta Mathematica},
	Issn = {1431-0635},
	Journal = {Doc. Math.},
	Mrclass = {11E72 (12G05 14L30)},
	Mrnumber = {MR2029168 (2004m:11056)},
	Mrreviewer = {Ryan Skip Garibaldi},
	Pages = {279--330 (electronic)},
	Title = {Essential dimension: a functorial point of view (after {A}.               {M}erkurjev)},
	Volume = {8},
	Year = {2003},
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@book{Blichfeldt1917Finite-Collinea,
	Author = {Blichfeldt, Hans F.},
	Date-Added = {2008-08-07 16:43:23 -0700},
	Date-Modified = {2008-08-07 16:45:40 -0700},
	Publisher = {The University of Chicago Press},
	Title = {Finite Collineation Groups},
	Year = {1917},
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@book{JensenLedetYui2002Generic-polynom,
	Address = {Cambridge},
	Author = {Jensen, Christian U. and Ledet, Arne and Yui, Noriko},
	Date-Added = {2008-08-07 09:51:22 -0700},
	Date-Modified = {2008-08-07 09:51:27 -0700},
	Isbn = {0-521-81998-9},
	Mrclass = {12F12 (13B05)},
	Mrnumber = {MR1969648 (2004d:12007)},
	Mrreviewer = {Jannis A. Antoniadis},
	Note = {Constructive aspects of the inverse Galois problem},
	Pages = {x+258},
	Publisher = {Cambridge University Press},
	Series = {Mathematical Sciences Research Institute Publications},
	Title = {Generic polynomials},
	Volume = {45},
	Year = {2002}}

@article{ReichsteinVonessen1995An-embedding-pr,
	Author = {Reichstein, Zinovy and Vonessen, Nikolaus},
	Coden = {JALGA4},
	Date-Added = {2008-08-07 09:41:47 -0700},
	Date-Modified = {2008-08-07 09:41:59 -0700},
	Fjournal = {Journal of Algebra},
	Issn = {0021-8693},
	Journal = {J. Algebra},
	Mrclass = {16K20 (12E15)},
	Mrnumber = {MR1355210 (96j:16011)},
	Mrreviewer = {B. Fein},
	Number = {2},
	Pages = {451--462},
	Title = {An embedding property of universal division algebras},
	Volume = {177},
	Year = {1995},
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@misc{DolgachevIskovskikh2006Finite-subgroup,
	Author = {Igor V. Dolgachev and Vasily A. Iskovskikh},
	Title = {Finite subgroups of the plane {C}remona group},
	Note = {arXiv:math/0610595v4 [math.AG]},
	Year = {2006},
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@article{KraftSchwarz2007Compression-of-,
	Author = {Kraft, Hanspeter and Schwarz, Gerald W.},
	Coden = {JALGA4},
	Date-Added = {2008-08-05 13:00:48 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Fjournal = {Journal of Algebra},
	Issn = {0021-8693},
	Journal = {J. Algebra},
	Mrclass = {14L30 (20C15)},
	Mrnumber = {MR2326147 (2008d:14070)},
	Mrreviewer = {Zinovy Reichstein},
	Number = {1},
	Pages = {268--291},
	Title = {Compression of finite group actions and covariant dimension},
	Volume = {313},
	Year = {2007},
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@article{Tokunaga2004Note-on-a-2-dim,
	Author = {Tokunaga, Hiro-o},
	Coden = {OJMAA7},
	Date-Added = {2008-08-04 17:37:18 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Fjournal = {Osaka Journal of Mathematics},
	Issn = {0030-6126},
	Journal = {Osaka J. Math.},
	Mrclass = {14E20 (14J27)},
	Mrnumber = {MR2116339 (2006a:14019)},
	Mrreviewer = {Feng-Wen An},
	Number = {4},
	Pages = {831--838},
	Title = {Note on a 2-dimensional versal {$D\sb 8$}-cover},
	Volume = {41},
	Year = {2004}}

@incollection{Tokunaga20052-dimensional-v,
	Address = {Paris},
	Author = {Tokunaga, Hiro-o},
	Booktitle = {Singularit\'es Franco-Japonaises},
	Date-Added = {2008-08-04 17:37:12 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Mrclass = {14J27 (14E20)},
	Mrnumber = {MR2145962 (2006e:14054)},
	Mrreviewer = {Tihomir A. Petrov},
	Pages = {307--322},
	Publisher = {Soc. Math. France},
	Series = {S\'emin. Congr.},
	Title = {2-dimensional versal {$S\sb 4$}-covers and rational elliptic               surfaces},
	Volume = {10},
	Year = {2005}}

@article{Tokunaga2006Two-dimensional,
	Author = {Tokunaga, Hiro-o},
	Date-Added = {2008-08-04 17:37:02 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Fjournal = {Kyushu Journal of Mathematics},
	Issn = {1340-6116},
	Journal = {Kyushu J. Math.},
	Mrclass = {14E20 (14E07 14L30)},
	Mrnumber = {MR2268246 (2007i:14017)},
	Mrreviewer = {Tommaso De Fernex},
	Number = {2},
	Pages = {439--456},
	Title = {Two-dimensional versal {$G$}-covers and {C}remona embeddings               of finite groups},
	Volume = {60},
	Year = {2006},
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@incollection{Serre2007Bounds-for-the-,
	Author = {Serre, Jean-Pierre},
	Booktitle = {Group representation theory},
	Date-Added = {2008-07-29 18:34:40 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Mrclass = {20H20},
	Mrnumber = {MR2336645 (2008g:20114)},
	Mrreviewer = {Robert M. Guralnick},
	Pages = {405--450},
	Publisher = {EPFL Press, Lausanne},
	Title = {Bounds for the orders of the finite subgroups of {$G(k)$}},
	Year = {2007},
	Bdsk-File-1 = {YnBsaXN0MDDUAQIDBAUGCQpYJHZlcnNpb25UJHRvcFkkYXJjaGl2ZXJYJG9iamVjdHMSAAGGoNE
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@article{KarpenkoMerkurjev2008Essential-dimen,
	Author = {Karpenko, Nikita A. and Merkurjev, Alexander S.},
	Coden = {INVMBH},
	Date-Added = {2008-07-10 09:50:49 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Fjournal = {Inventiones Mathematicae},
	Issn = {0020-9910},
	Journal = {Invent. Math.},
	Mrclass = {12F10 (14C35 16Kxx)},
	Mrnumber = {MR2393078},
	Number = {3},
	Pages = {491--508},
	Title = {Essential dimension of finite {$p$}-groups},
	Volume = {172},
	Year = {2008}}

@article{Bannai2007Construction-of,
	Author = {Bannai, Shinzo},
	Coden = {OJMAA7},
	Date-Added = {2008-07-10 09:49:57 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Fjournal = {Osaka Journal of Mathematics},
	Issn = {0030-6126},
	Journal = {Osaka J. Math.},
	Mrclass = {14E20 (14M25)},
	Mrnumber = {MR2313031 (2008g:14022)},
	Mrreviewer = {Ekaterina Amerik},
	Number = {1},
	Pages = {139--146},
	Title = {Construction of versal {G}alois coverings using toric               varieties},
	Volume = {44},
	Year = {2007},
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@article{ManinTsfasman1986Rational-variet,
	Author = {Manin, Yuri I. and Tsfasman, M. A.},
	Date-Added = {2008-07-10 09:47:53 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Fjournal = {Akademiya Nauk SSSR i Moskovskoe Matematicheskoe Obshchestvo.               Uspekhi Matematicheskikh Nauk},
	Issn = {0042-1316},
	Journal = {Uspekhi Mat. Nauk},
	Mrclass = {11G35 (14G05 14J20)},
	Mrnumber = {MR842161 (87k:11065)},
	Mrreviewer = {Daniel Coray},
	Number = {2(248)},
	Pages = {43--94},
	Title = {Rational varieties: algebra, geometry, arithmetic},
	Volume = {41},
	Year = {1986}}

@article{BannaiTokunaga2007A-note-on-embed,
	Author = {Bannai, Shinzo and Tokunaga, Hiro-o},
	Coden = {KRMPBV},
	Date-Added = {2008-07-10 09:46:35 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Fjournal = {Kyoto University. Research Institute for Mathematical               Sciences. Publications},
	Issn = {0034-5318},
	Journal = {Publ. Res. Inst. Math. Sci.},
	Mrclass = {14E20 (14E07)},
	Mrnumber = {MR2389794},
	Number = {4},
	Pages = {1111--1123},
	Title = {A note on embeddings of {$S\sb 4$} and {$A\sb 5$} into the               two-dimensional {C}remona group and versal {G}alois covers},
	Volume = {43},
	Year = {2007},
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@article{ReichsteinYoussin2000Essential-dimen,
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	Coden = {CJMAAB},
	Date-Added = {2008-07-10 09:45:09 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Fjournal = {Canadian Journal of Mathematics. Journal Canadien de               Math\'ematiques},
	Issn = {0008-414X},
	Journal = {Canad. J. Math.},
	Mrclass = {14L30 (14E15 20G15)},
	Mrnumber = {MR1782331 (2001k:14088)},
	Mrreviewer = {Lucy Moser-Jauslin},
	Note = {With an appendix by J\'anos Koll\'ar and Endre Szab\'o},
	Number = {5},
	Pages = {1018--1056},
	Title = {Essential dimensions of algebraic groups and a resolution               theorem for {$G$}-varieties},
	Volume = {52},
	Year = {2000}}

@article{Kolo-TelenKarpenkoMerkurev2007Rational-surfac,
	Author = {Kol'o-Telen, Zh.-L. and Karpenko, N. A. and Merkur'ev, A. S.},
	Date-Added = {2008-07-10 09:38:11 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Fjournal = {Rossi\u\i skaya Akademiya Nauk. Algebra i Analiz},
	Issn = {0234-0852},
	Journal = {Algebra i Analiz},
	Mrclass = {14Lxx (14J26)},
	Mrnumber = {MR2381945},
	Number = {5},
	Pages = {159--178},
	Title = {Rational surfaces and the canonical dimension of the group               {${\rm PGL}\sb 6$}},
	Volume = {19},
	Year = {2007}}

@article{BuhlerReichstein1997On-the-essentia,
	Author = {Buhler, Joe and Reichstein, Zinovy},
	Coden = {CMPMAF},
	Date-Added = {2008-07-10 09:36:35 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Fjournal = {Compositio Mathematica},
	Issn = {0010-437X},
	Journal = {Compositio Math.},
	Mrclass = {12F10 (12E05 14E05 14L30)},
	Mrnumber = {MR1457337 (98e:12004)},
	Mrreviewer = {Helmut V{\"o}lklein},
	Number = {2},
	Pages = {159--179},
	Title = {On the essential dimension of a finite group},
	Volume = {106},
	Year = {1997}}

@incollection{BuhlerReichstein1999On-Tschirnhaus-,
	Address = {Dordrecht},
	Author = {Buhler, Joe and Reichstein, Zinovy},
	Booktitle = {Topics in number theory (University Park, PA, 1997)},
	Date-Added = {2008-07-10 09:35:54 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Mrclass = {12E12 (11C08)},
	Mrnumber = {MR1691314 (2000b:12003)},
	Mrreviewer = {Maurice Mignotte},
	Pages = {127--142},
	Publisher = {Kluwer Acad. Publ.},
	Series = {Math. Appl.},
	Title = {On {T}schirnhaus transformations},
	Volume = {467},
	Year = {1999}}

@article{ReichsteinYoussin2002A-birational-in,
	Author = {Reichstein, Zinovy and Youssin, Boris},
	Coden = {PJMAAI},
	Date-Added = {2008-07-10 09:35:14 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Fjournal = {Pacific Journal of Mathematics},
	Issn = {0030-8730},
	Journal = {Pacific J. Math.},
	Mrclass = {14L30 (14E05)},
	Mrnumber = {MR1905199 (2003c:14052)},
	Mrreviewer = {Dennis Snow},
	Number = {1},
	Pages = {223--246},
	Title = {A birational invariant for algebraic group actions},
	Volume = {204},
	Year = {2002}}
	
@article {Roquette1964Isomorphisms-of,
    AUTHOR = {Roquette, Peter},
     TITLE = {Isomorphisms of generic splitting fields of simple algebras},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik},
    VOLUME = {214/215},
      YEAR = {1964},
     PAGES = {207--226},
      ISSN = {0075-4102},
   MRCLASS = {16.46},
  MRNUMBER = {MR0166215 (29 \#3492)},
MRREVIEWER = {S. A. Amitsur},
}

@article{Ledet2007Finite-groups-o,
	Author = {Ledet, Arne},
	Coden = {JALGA4},
	Date-Added = {2008-07-10 09:34:33 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Fjournal = {Journal of Algebra},
	Issn = {0021-8693},
	Journal = {J. Algebra},
	Mrclass = {12F10},
	Mrnumber = {MR2309876 (2008e:12002)},
	Mrreviewer = {Martin Epkenhans},
	Number = {1},
	Pages = {31--37},
	Title = {Finite groups of essential dimension one},
	Volume = {311},
	Year = {2007},
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@article{Reichstein2000On-the-notion-o,
	Author = {Reichstein, Zinovy},
	Date-Added = {2008-07-10 09:32:25 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Fjournal = {Transformation Groups},
	Issn = {1083-4362},
	Journal = {Transform. Groups},
	Mrclass = {20G15 (14L30)},
	Mrnumber = {MR1780933 (2001j:20073)},
	Mrreviewer = {Jorge A. Vargas},
	Number = {3},
	Pages = {265--304},
	Title = {On the notion of essential dimension for algebraic groups},
	Volume = {5},
	Year = {2000}}

@article{Beauville2007p-elementary-su,
	Author = {Beauville, Arnaud},
	Coden = {JALGA4},
	Date-Added = {2008-07-10 09:28:48 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Fjournal = {Journal of Algebra},
	Issn = {0021-8693},
	Journal = {J. Algebra},
	Mrclass = {14E07 (14J26)},
	Mrnumber = {MR2344578 (2008g:14019)},
	Mrreviewer = {Julie D{\'e}serti},
	Number = {2},
	Pages = {553--564},
	Title = {{$p$}-elementary subgroups of the {C}remona group},
	Volume = {314},
	Year = {2007}}

@article{Blanc2007Finite-abelian-,
	Author = {Blanc, J{\'e}r{\'e}my},
	Date-Added = {2008-07-10 09:28:10 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Fjournal = {Comptes Rendus Math\'ematique. Acad\'emie des Sciences. Paris},
	Issn = {1631-073X},
	Journal = {C. R. Math. Acad. Sci. Paris},
	Mrclass = {14E07 (14E05)},
	Mrnumber = {MR2286582 (2008b:14020)},
	Mrreviewer = {Julie D{\'e}serti},
	Number = {1},
	Pages = {21--26},
	Title = {Finite abelian subgroups of the {C}remona group of the plane},
	Volume = {344},
	Year = {2007}}

@incollection{Reichstein2004Compressions-of,
	Address = {Providence, RI},
	Author = {Reichstein, Zinovy},
	Booktitle = {Invariant theory in all characteristics},
	Date-Added = {2008-07-10 09:26:21 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Mrclass = {14L30},
	Mrnumber = {MR2066467},
	Pages = {199--202},
	Publisher = {Amer. Math. Soc.},
	Series = {CRM Proc. Lecture Notes},
	Title = {Compressions of group actions},
	Volume = {35},
	Year = {2004},
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@article{Miller1987The-maximum-ord,
	Author = {Miller, William},
	Coden = {AMMYAE},
	Date-Added = {2008-07-10 09:23:55 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Fjournal = {The American Mathematical Monthly},
	Issn = {0002-9890},
	Journal = {Amer. Math. Monthly},
	Mrclass = {20B05 (11N99 20D60)},
	Mrnumber = {MR935414 (89k:20005)},
	Number = {6},
	Pages = {497--506},
	Title = {The maximum order of an element of a finite symmetric group},
	Volume = {94},
	Year = {1987}}

@article {KraftLotscherSchwarz2009Compression-of-,
    AUTHOR = {Kraft, Hanspeter and L{\"o}tscher, Roland and Schwarz, Gerald
              W.},
     TITLE = {Compression of finite group actions and covariant dimension.
              {II}},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {322},
      YEAR = {2009},
    NUMBER = {1},
     PAGES = {94--107},
      ISSN = {0021-8693},
     CODEN = {JALGA4},
   MRCLASS = {14L30},
  MRNUMBER = {MR2526377 (2010d:14068)},
MRREVIEWER = {Zinovy Reichstein},
       DOI = {10.1016/j.jalgebra.2009.01.039},
       URL = {http://dx.doi.org/10.1016/j.jalgebra.2009.01.039},
}


@article{ReichsteinYoussin2001Splitting-field,
	Author = {Reichstein, Zinovy and Youssin, Boris},
	Coden = {PJMAAI},
	Date-Added = {2008-07-10 09:20:19 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Fjournal = {Pacific Journal of Mathematics},
	Issn = {0030-8730},
	Journal = {Pacific J. Math.},
	Mrclass = {14L30 (16K20)},
	Mrnumber = {MR1863413 (2003a:14070)},
	Mrreviewer = {Jean-Pierre Tignol},
	Number = {1},
	Pages = {207--249},
	Title = {Splitting fields of {$G$}-varieties},
	Volume = {200},
	Year = {2001}}

@article{ReichsteinYoussin2003A-non-split-tor,
	Author = {Reichstein, Zinovy and Youssin, Boris},
	Coden = {JALGA4},
	Date-Added = {2008-07-10 09:19:42 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Fjournal = {Journal of Algebra},
	Issn = {0021-8693},
	Journal = {J. Algebra},
	Mrclass = {14L30},
	Mrnumber = {MR1978650 (2004g:14052)},
	Mrreviewer = {Amnon Neeman},
	Number = {2},
	Pages = {255--261},
	Title = {A non-split torsor with trivial fixed point obstruction},
	Volume = {263},
	Year = {2003}}

@article{ReichsteinVonessen2006Group-actions-o,
	Author = {Reichstein, Zinovy and Vonessen, Nikolaus},
	Coden = {JALGA4},
	Date-Added = {2008-07-10 09:18:09 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Fjournal = {Journal of Algebra},
	Issn = {0021-8693},
	Journal = {J. Algebra},
	Mrclass = {16K20 (14L30)},
	Mrnumber = {MR2265511 (2007h:16022)},
	Mrreviewer = {Sergey V. Tikhonov},
	Number = {2},
	Pages = {1160--1192},
	Title = {Group actions on central simple algebras: a geometric approach},
	Volume = {304},
	Year = {2006}}

@article{Zhang2001Automorphisms-o,
	Author = {Zhang, De-Qi},
	Coden = {JALGA4},
	Date-Added = {2008-07-10 09:17:19 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Fjournal = {Journal of Algebra},
	Issn = {0021-8693},
	Journal = {J. Algebra},
	Mrclass = {14J50 (14E07 14J26)},
	Mrnumber = {MR1823774 (2002c:14064)},
	Mrreviewer = {Arnaud Beauville},
	Note = {With an appendix by I. Dolgachev},
	Number = {2},
	Pages = {560--589},
	Title = {Automorphisms of finite order on rational surfaces},
	Volume = {238},
	Year = {2001}}

@article{ArtinMumford1972Some-elementary,
	Author = {Artin, M. and Mumford, D.},
	Date-Added = {2008-07-10 09:16:04 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Fjournal = {Proceedings of the London Mathematical Society. Third Series},
	Issn = {0024-6115},
	Journal = {Proc. London Math. Soc. (3)},
	Mrclass = {14J10 (14F25)},
	Mrnumber = {MR0321934 (48 \#299)},
	Mrreviewer = {M. Nagata},
	Pages = {75--95},
	Title = {Some elementary examples of unirational varieties which are               not rational},
	Volume = {25},
	Year = {1972}}

@article{Saltman1984Noethers-proble,
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	Coden = {INVMBH},
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	Date-Modified = {2008-08-05 13:03:55 -0700},
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	Journal = {Invent. Math.},
	Mrclass = {13B02 (13A20)},
	Mrnumber = {MR751131 (85m:13006)},
	Mrreviewer = {Zensho Nakao},
	Number = {1},
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	Title = {Noether's problem over an algebraically closed field},
	Volume = {77},
	Year = {1984}}

@article{Dolgachev2008Reflection-grou,
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	Coden = {BAMOAD},
	Date-Added = {2008-07-10 09:09:34 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Fjournal = {American Mathematical Society. Bulletin. New Series},
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	Journal = {Bull. Amer. Math. Soc. (N.S.)},
	Mrclass = {20F55 (14E07 14H20 14J28)},
	Mrnumber = {MR2358376},
	Number = {1},
	Pages = {1--60 (electronic)},
	Title = {Reflection groups in algebraic geometry},
	Volume = {45},
	Year = {2008}}

@article{Carter1972Conjugacy-class,
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	Date-Added = {2008-07-10 09:08:04 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Fjournal = {Compositio Mathematica},
	Issn = {0010-437X},
	Journal = {Compositio Math.},
	Mrclass = {20H15 (17B20)},
	Mrnumber = {MR0318337 (47 \#6884)},
	Mrreviewer = {Juri A. Bahturin},
	Pages = {1--59},
	Title = {Conjugacy classes in the {W}eyl group},
	Volume = {25},
	Year = {1972},
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@book{Brown1982Cohomology-of-g,
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	Date-Added = {2007-03-20 13:58:23 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
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	Mrclass = {20-02 (18-01 20F32 20J05 55-01)},
	Mrnumber = {MR672956 (83k:20002)},
	Mrreviewer = {Ross Staffeldt},
	Pages = {x+306},
	Publisher = {Springer-Verlag},
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	Volume = {87},
	Year = {1982}}

@article{Kuroda2002The-infinitenes,
	Author = {Kuroda, Shigeru},
	Coden = {OJMAA7},
	Date-Added = {2007-03-20 13:18:42 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Fjournal = {Osaka Journal of Mathematics},
	Issn = {0030-6126},
	Journal = {Osaka J. Math.},
	Mrclass = {13P10 (13A50)},
	Mrnumber = {MR1932287 (2003k:13033)},
	Mrreviewer = {Robert James Shank},
	Number = {3},
	Pages = {665--680},
	Title = {The infiniteness of the {SAGBI} bases for certain invariant rings},
	Volume = {39},
	Year = {2002},
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@misc{Essen2003The-Solution-of,
	Author = {Arno van den Essen},
	Date-Added = {2007-03-16 16:24:42 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Month = {July},
	Title = {The Solution of the Tame Generators Conjecture According to Shestakov and Umirbaev},
	Year = {2003},
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@url{MilneClass-Field-The,
	Author = {J. S. Milne},
	Date-Added = {2007-03-16 16:22:36 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Title = {Class Field Theory},
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@url{MilneAlgebraic-Geome,
	Author = {J. S. Milne},
	Date-Added = {2007-03-16 16:20:54 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Title = {Algebraic Geometry},
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@misc{SweedlerIdeal-Bases-and,
	Author = {Moss Sweedler},
	Date-Added = {2007-03-16 16:11:56 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Title = {Ideal Bases and Valuation Rings},
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@misc{MosteigSweedlerValuations-and-,
	Author = {Edward Mosteig and Moss Sweedler},
	Date-Added = {2007-03-16 15:50:43 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Title = {Valuations and Filtrations},
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@book{Connes1994Noncommutative-,
	Address = {San Diego, CA},
	Author = {Connes, Alain},
	Date-Added = {2007-03-16 15:49:39 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Isbn = {0-12-185860-X},
	Mrclass = {46Lxx (19K56 22D25 58B30 58G12 81T13 81V22 81V70)},
	Mrnumber = {MR1303779 (95j:46063)},
	Mrreviewer = {John Roe},
	Pages = {xiv+661},
	Publisher = {Academic Press Inc.},
	Title = {Noncommutative geometry},
	Year = {1994},
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@article{BrunsGubeladzeTrung2002Problems-and-al,
	Author = {Bruns, Winfried and Gubeladze, Joseph and Trung, Ng{\^o} Vi{\^e}t},
	Coden = {SMGFAN},
	Date-Added = {2007-03-16 15:46:58 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Fjournal = {Semigroup Forum},
	Issn = {0037-1912},
	Journal = {Semigroup Forum},
	Mrclass = {20M14 (13P10 20M25 52B20)},
	Mrnumber = {MR1876854 (2002m:20096)},
	Mrreviewer = {Rafael H. Villarreal},
	Number = {2},
	Pages = {180--212},
	Title = {Problems and algorithms for affine semigroups},
	Volume = {64},
	Year = {2002},
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@article{Grothendieck1967Elements-de-geo,
	Author = {Grothendieck, A.},
	Date-Added = {2007-03-16 15:43:13 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Fjournal = {Institut des Hautes \'Etudes Scientifiques. Publications Math\'ematiques},
	Issn = {0073-8301},
	Journal = {Inst. Hautes \'Etudes Sci. Publ. Math.},
	Mrclass = {14.55},
	Mrnumber = {MR0238860 (39 \#220)},
	Mrreviewer = {J. P. Murre},
	Number = {32},
	Pages = {361},
	Title = {\'{E}l\'ements de g\'eom\'etrie alg\'ebrique. {IV}. \'{E}tude locale des sch\'emas et des morphismes de sch\'emas {IV}},
	Year = {1967},
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@article{Grothendieck1966Elements-de-geo,
	Author = {Grothendieck, A.},
	Date-Added = {2007-03-16 15:43:13 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Fjournal = {Institut des Hautes \'Etudes Scientifiques. Publications Math\'ematiques},
	Issn = {0073-8301},
	Journal = {Inst. Hautes \'Etudes Sci. Publ. Math.},
	Mrclass = {14.55},
	Mrnumber = {MR0217086 (36 \#178)},
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	Title = {\'{E}l\'ements de g\'eom\'etrie alg\'ebrique. {IV}. \'{E}tude locale des sch\'emas et des morphismes de sch\'emas. {III}},
	Year = {1966},
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@article{Grothendieck1965Elements-de-geo,
	Author = {Grothendieck, A.},
	Date-Added = {2007-03-16 15:43:13 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Fjournal = {Institut des Hautes \'Etudes Scientifiques. Publications Math\'ematiques},
	Issn = {0073-8301},
	Journal = {Inst. Hautes \'Etudes Sci. Publ. Math.},
	Mrclass = {14.00},
	Mrnumber = {MR0199181 (33 \#7330)},
	Mrreviewer = {H. Hironaka},
	Number = {24},
	Pages = {231},
	Title = {\'{E}l\'ements de g\'eom\'etrie alg\'ebrique. {IV}. \'{E}tude locale des sch\'emas et des morphismes de sch\'emas. {II}},
	Year = {1965},
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@article{Grothendieck1964Elements-de-geo,
	Author = {Grothendieck, A.},
	Date-Added = {2007-03-16 15:43:13 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Fjournal = {Institut des Hautes \'Etudes Scientifiques. Publications Math\'ematiques},
	Issn = {0073-8301},
	Journal = {Inst. Hautes \'Etudes Sci. Publ. Math.},
	Mrclass = {14.05 (13.10)},
	Mrnumber = {MR0173675 (30 \#3885)},
	Mrreviewer = {H. Hironaka},
	Number = {20},
	Pages = {259},
	Title = {\'{E}l\'ements de g\'eom\'etrie alg\'ebrique. {IV}. \'{E}tude locale des sch\'emas et des morphismes de sch\'emas. {I}},
	Year = {1964},
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@article{Grothendieck1963Elements-de-geo,
	Author = {Grothendieck, A.},
	Date-Added = {2007-03-16 15:43:13 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Fjournal = {Institut des Hautes \'Etudes Scientifiques. Publications Math\'ematiques},
	Issn = {0073-8301},
	Journal = {Inst. Hautes \'Etudes Sci. Publ. Math.},
	Mrclass = {14.05},
	Mrnumber = {MR0163911 (29 \#1210)},
	Mrreviewer = {H. Hironaka},
	Number = {17},
	Pages = {91},
	Title = {\'{E}l\'ements de g\'eom\'etrie alg\'ebrique. {III}. \'{E}tude cohomologique des faisceaux coh\'erents. {II}},
	Year = {1963},
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@article{Grothendieck1961Elements-de-geo,
	Author = {Grothendieck, A.},
	Date-Added = {2007-03-16 15:43:13 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Fjournal = {Institut des Hautes \'Etudes Scientifiques. Publications Math\'ematiques},
	Issn = {0073-8301},
	Journal = {Inst. Hautes \'Etudes Sci. Publ. Math.},
	Mrclass = {14.05},
	Mrnumber = {MR0163910 (29 \#1209)},
	Number = {11},
	Pages = {167},
	Title = {\'{E}l\'ements de g\'eom\'etrie alg\'ebrique. {III}. \'{E}tude cohomologique des faisceaux coh\'erents. {I}},
	Year = {1961},
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@article{Grothendieck1961Elements-de-geo,
	Author = {Grothendieck, A.},
	Date-Added = {2007-03-16 15:43:13 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Fjournal = {Institut des Hautes \'Etudes Scientifiques. Publications Math\'ematiques},
	Issn = {0073-8301},
	Journal = {Inst. Hautes \'Etudes Sci. Publ. Math.},
	Mrclass = {14.05},
	Mrnumber = {MR0163909 (29 \#1208)},
	Number = {8},
	Pages = {222},
	Title = {\'{E}l\'ements de g\'eom\'etrie alg\'ebrique. {II}. \'{E}tude globale \'el\'ementaire de quelques classes de morphismes},
	Year = {1961},
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@article{Grothendieck1960Elements-de-geo,
	Author = {Grothendieck, A.},
	Date-Added = {2007-03-16 15:43:13 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Fjournal = {Institut des Hautes \'Etudes Scientifiques. Publications Math\'ematiques},
	Issn = {0073-8301},
	Journal = {Inst. Hautes \'Etudes Sci. Publ. Math.},
	Mrclass = {14.05},
	Mrnumber = {MR0163908 (29 \#1207)},
	Number = {4},
	Pages = {228},
	Title = {\'{E}l\'ements de g\'eom\'etrie alg\'ebrique. {I}. {L}e langage des sch\'emas},
	Year = {1960},
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@book {Segre1942The-Non-singula,
    AUTHOR = {Segre, B.},
     TITLE = {The {N}on-singular {C}ubic {S}urfaces},
 PUBLISHER = {Oxford University Press},
   ADDRESS = {Oxford},
      YEAR = {1942},
     PAGES = {xi+180},
   MRCLASS = {14.0X},
  MRNUMBER = {MR0008171 (4,254b)},
MRREVIEWER = {O. Zariski},
}

@book{Fulton1993Introduction-to,
	Address = {Princeton, NJ},
	Author = {Fulton, William},
	Date-Added = {2007-01-31 11:29:05 -0800},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Isbn = {0-691-00049-2},
	Mrclass = {14M25 (14-02 14J30)},
	Mrnumber = {MR1234037 (94g:14028)},
	Mrreviewer = {T. Oda},
	Note = {The William H. Roever Lectures in Geometry},
	Pages = {xii+157},
	Publisher = {Princeton University Press},
	Series = {Annals of Mathematics Studies},
	Title = {Introduction to toric varieties},
	Volume = {131},
	Year = {1993}}

@article{Gobel1999The-optimal-low,
	Author = {G\"obel, Manfred},
	Date-Added = {2007-01-31 11:10:18 -0800},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Fjournal = {Discrete Mathematics \& Theoretical Computer Science. DMTCS. An Electronic Journal},
	Issn = {1365-8050},
	Journal = {Discrete Math. Theor. Comput. Sci.},
	Mrclass = {13A50},
	Mrnumber = {MR1695195 (2001b:13008)},
	Number = {2},
	Pages = {65--70 (electronic)},
	Title = {The optimal lower bound for generators of invariant rings without finite {SAGBI} bases with respect to any admissible order},
	Volume = {3},
	Year = {1999},
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@article{TrandHoa1986Affine-Semigrou,
	Author = {Ngo Viet Trand and Le Tuan Hoa},
	Date-Added = {2007-01-26 14:54:27 -0800},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Journal = {Trans. Amer. Math. Soc.},
	Month = {November},
	Number = {1},
	Pages = {145-167},
	Title = {Affine Semigroups and Cohen-Macauley Rings Generated by Monomials},
	Volume = {298},
	Year = {1986},
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@article{Dickson1913Finiteness-of-t,
	Author = {Dickson, Leonard Eugene},
	Date-Added = {2007-01-17 12:25:14 -0800},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Journal = {American Journal of Mathematics},
	Number = {4},
	Pages = {413-422},
	Title = {Finiteness of the Odd Perfect and Primitive Abundant Numbers with n Distinct Prime Factors},
	Volume = {35},
	Year = {1913},
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@article{Johnstone1983The-point-of-po,
	Author = {Johnstone, Peter T.},
	Coden = {BAMOAD},
	Date-Added = {2006-12-09 14:41:19 -0800},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Fjournal = {American Mathematical Society. Bulletin. New Series},
	Issn = {0273-0979},
	Journal = {Bull. Amer. Math. Soc. (N.S.)},
	Mrclass = {01A65 (18B25 54A05)},
	Mrnumber = {MR682820 (84f:01043)},
	Mrreviewer = {Marta C. Bunge},
	Number = {1},
	Pages = {41--53},
	Title = {The point of pointless topology},
	Volume = {8},
	Year = {1983},
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@electronic{LakshmibaiConnecting-Inva,
	Author = {Lakshmibai, V.},
	Date-Added = {2006-11-26 16:49:23 -0800},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Title = {Connecting Invariant Theory and NP-Completeness},
	Urldate = {2005},
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@article{Regan2002Understanding-t,
	Author = {Regan, Kenneth W.},
	Date-Added = {2006-11-26 16:46:21 -0800},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Fjournal = {Bulletin of the European Association for Theoretical Computer Science. EATCS},
	Issn = {0252-9742},
	Journal = {Bull. Eur. Assoc. Theor. Comput. Sci. EATCS},
	Mrclass = {68Q15},
	Mrnumber = {MR1964501 (2004b:68060)},
	Number = {78},
	Pages = {86--99},
	Title = {Understanding the {M}ulmuley-{S}ohoni approach to {P} vs. {NP}},
	Year = {2002},
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@incollection{RobbianoSweedler1990Subalgebra-base,
	Address = {Berlin},
	Author = {Robbiano, Lorenzo and Sweedler, Moss},
	Booktitle = {Commutative algebra (Salvador, 1988)},
	Date-Added = {2006-10-12 20:46:30 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Mrclass = {13P10},
	Mrnumber = {MR1068324 (91f:13027)},
	Mrreviewer = {Ralf Fr{\"o}berg},
	Pages = {61--87},
	Publisher = {Springer},
	Series = {Lecture Notes in Math.},
	Title = {Subalgebra bases},
	Volume = {1430},
	Year = {1990}}

@phdthesis{Tesemma2004On-Multiplicati,
	Author = {Tesemma, Mohammed},
	Date-Added = {2006-10-10 16:25:06 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	School = {Spelman College},
	Title = {On Multiplicative Invariants of Finite Reflection Groups},
	Year = {2004}}

@book{ZariskiSamuel1975Commutative-alg,
	Address = {New York},
	Author = {Zariski, Oscar and Samuel, Pierre},
	Date-Added = {2006-10-06 15:07:27 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Mrclass = {13-02 (12JXX 14-02)},
	Mrnumber = {MR0389876 (52 \#10706)},
	Note = {Reprint of the 1960 edition, Graduate Texts in Mathematics, Vol. 29},
	Pages = {x+414},
	Publisher = {Springer-Verlag},
	Title = {Commutative algebra. {V}ol. {II}},
	Year = {1975}}

@book{ZariskiSamuel1975Commutative-alg,
	Address = {New York},
	Author = {Zariski, Oscar and Samuel, Pierre},
	Date-Added = {2006-10-06 15:07:27 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Mrclass = {13-02},
	Mrnumber = {MR0384768 (52 \#5641)},
	Note = {With the cooperation of I. S. Cohen, Corrected reprinting of the 1958 edition, Graduate Texts in Mathematics, No. 28},
	Pages = {xi+329},
	Publisher = {Springer-Verlag},
	Title = {Commutative algebra. {V}ol. 1},
	Year = {1975}}

@article{Barge1997Cohomologie-des,
	Author = {Barge, Jean},
	Coden = {COMHAX},
	Date-Added = {2006-10-03 12:39:23 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Fjournal = {Commentarii Mathematici Helvetici},
	Issn = {0010-2571},
	Journal = {Comment. Math. Helv.},
	Mrclass = {12G05 (03C60)},
	Mrnumber = {MR1456312 (98g:12006)},
	Mrreviewer = {Claus Scheiderer},
	Number = {1},
	Pages = {1--15},
	Title = {Cohomologie des groupes et corps d'invariants multiplicatifs tordus},
	Volume = {72},
	Year = {1997},
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@book {Coxeter1991Regular-complex,
    AUTHOR = {Coxeter, Harold S. M.},
     TITLE = {Regular complex polytopes},
   EDITION = {Second},
 PUBLISHER = {Cambridge University Press},
   ADDRESS = {Cambridge},
      YEAR = {1991},
     PAGES = {xiv+210},
      ISBN = {0-521-39490-2},
   MRCLASS = {51M20 (52B15)},
  MRNUMBER = {MR1119304 (92h:51035)},
MRREVIEWER = {P. McMullen},
}

@book{CoxLittleOShea2005Using-algebraic,
	Address = {New York},
	Author = {Cox, David A. and Little, John and O'Shea, Donal},
	Date-Added = {2006-10-02 14:14:50 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Edition = {Second},
	Isbn = {0-387-20706-6},
	Mrclass = {13Pxx (13-01 14-01 14Qxx)},
	Mrnumber = {MR2122859 (2005i:13037)},
	Pages = {xii+572},
	Publisher = {Springer},
	Series = {Graduate Texts in Mathematics},
	Title = {Using algebraic geometry},
	Volume = {185},
	Year = {2005}}

@book{Serre1977Linear-represen,
	Address = {New York},
	Author = {Serre, Jean-Pierre},
	Date-Added = {2006-10-02 14:14:50 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Isbn = {0-387-90190-6},
	Mrclass = {20CXX},
	Mrnumber = {MR0450380 (56 \#8675)},
	Mrreviewer = {W. Feit},
	Note = {Translated from the second French edition by Leonard L. Scott, Graduate Texts in Mathematics, Vol. 42},
	Pages = {x+170},
	Publisher = {Springer-Verlag},
	Title = {Linear representations of finite groups},
	Year = {1977}}

@incollection{ThieryThomasse2004Convex-cones-an,
	Address = {Providence, RI},
	Author = {Thi{\'e}ry, N. M. and Thomass{\'e}, S.},
	Booktitle = {Invariant theory in all characteristics},
	Date-Added = {2006-10-02 08:29:01 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Keywords = {SAGBI Bases},
	Mrclass = {13A50 (52B20)},
	Mrnumber = {MR2066473 (2005e:13006)},
	Mrreviewer = {Robert James Shank},
	Pages = {259--263},
	Publisher = {Amer. Math. Soc.},
	Series = {CRM Proc. Lecture Notes},
	Title = {Convex cones and {SAGBI} bases of permutation invariants},
	Volume = {35},
	Year = {2004}}

@article{ShankWehlau2002Computing-modul,
	Author = {Shank, R. James and Wehlau, David L.},
	Date-Added = {2006-10-02 08:29:01 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Fjournal = {Journal of Symbolic Computation},
	Issn = {0747-7171},
	Journal = {J. Symbolic Comput.},
	Keywords = {Invariant Theory},
	Mrclass = {13A50 (13P10)},
	Mrnumber = {MR1937464 (2003j:13006)},
	Mrreviewer = {Angelina Chin},
	Number = {5},
	Pages = {307--327},
	Title = {Computing modular invariants of {$p$}-groups},
	Volume = {34},
	Year = {2002},
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@incollection{KapurMadlener1989A-completion-pr,
	Address = {New York},
	Author = {Kapur, Deepak and Madlener, Klaus},
	Booktitle = {Computers and mathematics (Cambridge, MA, 1989)},
	Date-Added = {2006-10-02 08:23:06 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Mrclass = {13-04 (13A15 13B25 68Q40)},
	Mrnumber = {MR1005954 (90g:13001)},
	Mrreviewer = {Bernd Sturmfels},
	Pages = {1--11},
	Publisher = {Springer},
	Title = {A completion procedure for computing a canonical basis for a {$k$}-subalgebra},
	Year = {1989}}

@article{Robbiano1986On-the-theory-o,
	Author = {Robbiano, Lorenzo},
	Date-Added = {2006-10-02 08:23:06 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Fjournal = {Journal of Symbolic Computation},
	Issn = {0747-7171},
	Journal = {J. Symbolic Comput.},
	Keywords = {Gr{\"o}bner Bases},
	Mrclass = {13C05 (13-04 13A15 18D35 68Q40)},
	Mrnumber = {MR849048 (87j:13010)},
	Mrreviewer = {Manfred Herrmann},
	Number = {2},
	Pages = {139--170},
	Title = {On the theory of graded structures},
	Volume = {2},
	Year = {1986}}

@book{Ewald1996Combinatorial-c,
	Address = {New York},
	Author = {Ewald, G{\"u}nter},
	Date-Added = {2006-10-02 08:17:21 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Isbn = {0-387-94755-8},
	Mrclass = {52B20 (14M25 52B05)},
	Mrnumber = {MR1418400 (97i:52012)},
	Mrreviewer = {P. McMullen},
	Pages = {xiv+372},
	Publisher = {Springer-Verlag},
	Series = {Graduate Texts in Mathematics},
	Title = {Combinatorial convexity and algebraic geometry},
	Volume = {168},
	Year = {1996}}

@article{ConcaHerzogValla1996Sagbi-bases-wit,
	Author = {Conca, Aldo and Herzog, J{\"u}rgen and Valla, Giuseppe},
	Coden = {JRMAA8},
	Date-Added = {2006-10-02 08:17:21 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Fjournal = {Journal f\"ur die Reine und Angewandte Mathematik},
	Issn = {0075-4102},
	Journal = {J. Reine Angew. Math.},
	Mrclass = {13P10 (13A30)},
	Mrnumber = {MR1390693 (97h:13023)},
	Mrreviewer = {Ng{\^o} Vi{\^e}t Trung},
	Pages = {113--138},
	Title = {Sagbi bases with applications to blow-up algebras},
	Volume = {474},
	Year = {1996}}

@book{Grillet1995Semigroups,
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	Date-Added = {2006-10-02 08:17:21 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Isbn = {0-8247-9662-4},
	Mrclass = {20M10 (20M14 20M17 20M18 20M35)},
	Mrnumber = {MR1350793 (96k:20122)},
	Mrreviewer = {M{\'a}ria B. Szendrei},
	Note = {An introduction to the structure theory},
	Pages = {xii+398},
	Publisher = {Marcel Dekker Inc.},
	Series = {Monographs and Textbooks in Pure and Applied Mathematics},
	Title = {Semigroups},
	Volume = {193},
	Year = {1995}}

@book{Gilmer1984Commutative-sem,
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	Author = {Gilmer, Robert},
	Date-Added = {2006-10-02 08:17:21 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Isbn = {0-226-29391-2; 0-226-29392-0},
	Mrclass = {20M25 (13-02 20-02)},
	Mrnumber = {MR741678 (85e:20058)},
	Mrreviewer = {M. Teply},
	Pages = {xii+380},
	Publisher = {University of Chicago Press},
	Series = {Chicago Lectures in Mathematics},
	Title = {Commutative semigroup rings},
	Year = {1984}}

@book{Lorenz2005Multiplicative-,
	Address = {Berlin},
	Author = {Lorenz, Martin},
	Date-Added = {2006-10-02 07:58:43 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Isbn = {3-540-24323-2},
	Keywords = {Invariant Theory},
	Mrclass = {13A50 (12F20 13H10 20F55)},
	Mrnumber = {MR2131760 (2005m:13012)},
	Mrreviewer = {Frank D. Grosshans},
	Note = {Invariant Theory and Algebraic Transformation Groups, VI},
	Pages = {xii+177},
	Publisher = {Springer-Verlag},
	Series = {Encyclopaedia of Mathematical Sciences},
	Title = {Multiplicative invariant theory},
	Volume = {135},
	Year = {2005}}

@book{Sturmfels2002Solving-systems,
	Author = {Sturmfels, Bernd},
	Date-Added = {2006-10-02 07:58:43 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Isbn = {0-8218-3251-4},
	Mrclass = {13P10 (14P99 14Q15 62-09 65H10)},
	Mrnumber = {MR1925796 (2003i:13037)},
	Mrreviewer = {Joseph Gubeladze},
	Pages = {viii+152},
	Publisher = {Published for the Conference Board of the Mathematical Sciences, Washington, DC},
	Series = {CBMS Regional Conference Series in Mathematics},
	Title = {Solving systems of polynomial equations},
	Volume = {97},
	Year = {2002}}

@book{DerksenKemper2002Computational-i,
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	Author = {Derksen, Harm and Kemper, Gregor},
	Date-Added = {2006-10-02 07:58:43 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Isbn = {3-540-43476-3},
	Keywords = {Invariant Theory},
	Mrclass = {13A50 (13P10)},
	Mrnumber = {MR1918599 (2003g:13004)},
	Mrreviewer = {Dmitri I. Panyushev},
	Note = {Encyclopaedia of Mathematical Sciences, 130},
	Pages = {x+268},
	Publisher = {Springer-Verlag},
	Series = {Invariant Theory and Algebraic Transformation Groups, I},
	Title = {Computational invariant theory},
	Year = {2002}}

@book{Lang2002Algebra,
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	Author = {Lang, Serge},
	Date-Added = {2006-10-02 07:58:43 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Edition = {third},
	Isbn = {0-387-95385-X},
	Mrclass = {00A05 (15-02)},
	Mrnumber = {MR1878556 (2003e:00003)},
	Pages = {xvi+914},
	Publisher = {Springer-Verlag},
	Series = {Graduate Texts in Mathematics},
	Title = {Algebra},
	Volume = {211},
	Year = {2002}}

@book{Harpe2000Topics-in-geome,
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	Author = {de la Harpe, Pierre},
	Date-Added = {2006-10-02 07:58:43 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Isbn = {0-226-31719-6; 0-226-31721-8},
	Mrclass = {20F65 (20F69 57M07)},
	Mrnumber = {MR1786869 (2001i:20081)},
	Mrreviewer = {Lee Mosher},
	Pages = {vi+310},
	Publisher = {University of Chicago Press},
	Series = {Chicago Lectures in Mathematics},
	Title = {Topics in geometric group theory},
	Year = {2000}}

@book{Folland1999Real-analysis,
	Address = {New York},
	Author = {Folland, Gerald B.},
	Date-Added = {2006-10-02 07:58:43 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Edition = {Second},
	Isbn = {0-471-31716-0},
	Mrclass = {00A05 (26-01 28-01 46-01)},
	Mrnumber = {MR1681462 (2000c:00001)},
	Note = {Modern techniques and their applications, A Wiley-Interscience Publication},
	Pages = {xvi+386},
	Publisher = {John Wiley \& Sons Inc.},
	Series = {Pure and Applied Mathematics (New York)},
	Title = {Real analysis},
	Year = {1999}}

@book{Mac-Lane1998Categories-for-,
	Address = {New York},
	Author = {Mac Lane, Saunders},
	Date-Added = {2006-10-02 07:58:43 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Edition = {Second},
	Isbn = {0-387-98403-8},
	Mrclass = {18-02},
	Mrnumber = {MR1712872 (2001j:18001)},
	Pages = {xii+314},
	Publisher = {Springer-Verlag},
	Series = {Graduate Texts in Mathematics},
	Title = {Categories for the working mathematician},
	Volume = {5},
	Year = {1998}}

@book{CoxLittleOShea1997Ideals-varietie,
	Address = {New York},
	Author = {Cox, David and Little, John and O'Shea, Donal},
	Date-Added = {2006-10-02 07:58:43 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Edition = {Second},
	Isbn = {0-387-94680-2},
	Keywords = {Gr{\"o}bner Bases},
	Mrclass = {13P10 (13-01 14-01 14Qxx 68Q40)},
	Mrnumber = {MR1417938 (97h:13024)},
	Note = {An introduction to computational algebraic geometry and commutative algebra},
	Pages = {xiv+536},
	Publisher = {Springer-Verlag},
	Series = {Undergraduate Texts in Mathematics},
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	Year = {1997}}

@book{Sturmfels1996Grobner-bases-a,
	Address = {Providence, RI},
	Author = {Sturmfels, Bernd},
	Date-Added = {2006-10-02 07:58:43 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Isbn = {0-8218-0487-1},
	Keywords = {Gr{\"o}bner Bases},
	Mrclass = {13P10 (14M25 52B20)},
	Mrnumber = {MR1363949 (97b:13034)},
	Mrreviewer = {P. Schenzel},
	Pages = {xii+162},
	Publisher = {American Mathematical Society},
	Series = {University Lecture Series},
	Title = {Gr\"obner bases and convex polytopes},
	Volume = {8},
	Year = {1996}}

@book{Shafarevich1994Basic-algebraic,
	Address = {Berlin},
	Author = {Shafarevich, Igor R.},
	Date-Added = {2006-10-02 07:58:43 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Edition = {Second},
	Isbn = {3-540-54812-2},
	Mrclass = {14-01},
	Mrnumber = {MR1328833 (95m:14001)},
	Note = {Varieties in projective space, Translated from the 1988 Russian edition and with notes by Miles Reid},
	Pages = {xx+303},
	Publisher = {Springer-Verlag},
	Title = {Basic algebraic geometry. 1},
	Year = {1994}}

@book{Weibel1994An-introduction,
	Address = {Cambridge},
	Author = {Weibel, Charles A.},
	Date-Added = {2006-10-02 07:58:43 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Isbn = {0-521-43500-5; 0-521-55987-1},
	Mrclass = {18-01 (16-01 17-01 20-01 55Uxx)},
	Mrnumber = {MR1269324 (95f:18001)},
	Mrreviewer = {Kenneth A. Brown},
	Pages = {xiv+450},
	Publisher = {Cambridge University Press},
	Series = {Cambridge Studies in Advanced Mathematics},
	Title = {An introduction to homological algebra},
	Volume = {38},
	Year = {1994}}

@book{Devlin1993The-joy-of-sets,
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	Author = {Devlin, Keith},
	Date-Added = {2006-10-02 07:58:43 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Edition = {Second},
	Isbn = {0-387-94094-4},
	Mrclass = {03-01},
	Mrnumber = {MR1237397 (94e:03001)},
	Note = {Fundamentals of contemporary set theory},
	Pages = {x+192},
	Publisher = {Springer-Verlag},
	Series = {Undergraduate Texts in Mathematics},
	Title = {The joy of sets},
	Year = {1993}}

@book{DummitFoote1991Abstract-algebr,
	Address = {Englewood Cliffs, NJ},
	Author = {Dummit, David S. and Foote, Richard M.},
	Date-Added = {2006-10-02 07:58:43 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Isbn = {0-13-004771-6},
	Mrclass = {00A05 (16-01 20-01)},
	Mrnumber = {MR1138725 (92k:00007)},
	Mrreviewer = {N. Popescu},
	Pages = {xiv+658},
	Publisher = {Prentice Hall Inc.},
	Title = {Abstract algebra},
	Year = {1991}}

@book{Humphreys1978Introduction-to,
	Address = {New York},
	Author = {Humphreys, James E.},
	Date-Added = {2006-10-02 07:58:43 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Isbn = {0-387-90053-5},
	Mrclass = {17Bxx},
	Mrnumber = {MR499562 (81b:17007)},
	Mrreviewer = {I. P. Shestakov},
	Note = {Second printing, revised},
	Pages = {xii+171},
	Publisher = {Springer-Verlag},
	Series = {Graduate Texts in Mathematics},
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	Volume = {9},
	Year = {1978}}

@book{AtiyahMacdonald1969Introduction-to,
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	Date-Added = {2006-10-02 07:58:43 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
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	Mrnumber = {MR0242802 (39 \#4129)},
	Mrreviewer = {J. A. Johnson},
	Pages = {ix+128},
	Publisher = {Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont.},
	Title = {Introduction to commutative algebra},
	Year = {1969}}

@book{Hatcher2002Algebraic-topol,
	Address = {Cambridge},
	Author = {Hatcher, Allen},
	Date-Added = {2006-10-02 07:51:48 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Isbn = {0-521-79160-X; 0-521-79540-0},
	Mrclass = {55-01 (55-00)},
	Mrnumber = {MR1867354 (2002k:55001)},
	Mrreviewer = {Donald W. Kahn},
	Pages = {xii+544},
	Publisher = {Cambridge University Press},
	Title = {Algebraic topology},
	Year = {2002}}

@book{Olver1999Classical-invar,
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	Author = {Olver, Peter J.},
	Date-Added = {2006-10-02 07:51:48 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Isbn = {0-521-55821-2},
	Keywords = {Invariant Theory},
	Mrclass = {13A50 (58J70)},
	Mrnumber = {MR1694364 (2001g:13009)},
	Mrreviewer = {Jan A. Sanders},
	Pages = {xxii+280},
	Publisher = {Cambridge University Press},
	Series = {London Mathematical Society Student Texts},
	Title = {Classical invariant theory},
	Volume = {44},
	Year = {1999}}

@book{FriedbergInselSpence1997Linear-algebra,
	Address = {Upper Saddle River, NJ},
	Author = {Friedberg, Stephen H. and Insel, Arnold J. and Spence, Lawrence E.},
	Date-Added = {2006-10-02 07:51:48 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Edition = {Third},
	Isbn = {0-13-233859-9},
	Mrclass = {15-01},
	Mrnumber = {MR1434064},
	Pages = {xiv+557},
	Publisher = {Prentice Hall Inc.},
	Title = {Linear algebra},
	Year = {1997}}

@book{Arnolcprimed1992Ordinary-differ,
	Address = {Berlin},
	Author = {Arnol{\cprime}d, Vladimir I.},
	Date-Added = {2006-10-02 07:51:48 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Isbn = {3-540-54813-0},
	Mrclass = {34-01 (34Cxx 58-01)},
	Mrnumber = {MR1162307 (93b:34001)},
	Note = {Translated from the third Russian edition by Roger Cooke},
	Pages = {334},
	Publisher = {Springer-Verlag},
	Series = {Springer Textbook},
	Title = {Ordinary differential equations},
	Year = {1992}}

@book{Rudin1987Real-and-comple,
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	Author = {Rudin, Walter},
	Date-Added = {2006-10-02 07:51:48 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Edition = {Third},
	Isbn = {0-07-054234-1},
	Mrclass = {00A05 (26-01 30-01 46-01)},
	Mrnumber = {MR924157 (88k:00002)},
	Pages = {xiv+416},
	Publisher = {McGraw-Hill Book Co.},
	Title = {Real and complex analysis},
	Year = {1987}}

@book{HardyWright1979An-introduction,
	Address = {New York},
	Author = {Hardy, G. H. and Wright, E. M.},
	Date-Added = {2006-10-02 07:51:48 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Edition = {Fifth},
	Isbn = {0-19-853170-2; 0-19-853171-0},
	Mrclass = {10-01},
	Mrnumber = {MR568909 (81i:10002)},
	Mrreviewer = {T. M. Apostol},
	Pages = {xvi+426},
	Publisher = {The Clarendon Press Oxford University Press},
	Title = {An introduction to the theory of numbers},
	Year = {1979}}

@book{Spivak1965Calculus-on-man,
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	Date-Added = {2006-10-02 07:51:48 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Mrclass = {26.20 (57.00)},
	Mrnumber = {MR0209411 (35 \#309)},
	Mrreviewer = {C. B. Allendoerfer},
	Pages = {xii+144},
	Publisher = {W. A. Benjamin, Inc., New York-Amsterdam},
	Title = {Calculus on manifolds. {A} modern approach to classical theorems of advanced calculus},
	Year = {1965}}

@book{Artin1991Algebra,
	Address = {Englewood Cliffs, NJ},
	Author = {Artin, Michael},
	Date-Added = {2006-10-02 07:45:08 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Isbn = {0-13-004763-5},
	Mrclass = {00A05 (11-01 12-01 13-01 15-01 16-01 20-01)},
	Mrnumber = {MR1129886 (92g:00001)},
	Mrreviewer = {Gerald J. Janusz},
	Pages = {xviii+618},
	Publisher = {Prentice Hall Inc.},
	Title = {Algebra},
	Year = {1991}}

@incollection{Robbiano1985Term-orderings-,
	Address = {Berlin},
	Author = {Robbiano, Lorenzo},
	Booktitle = {EUROCAL '85, Vol.\ 2 (Linz, 1985)},
	Date-Added = {2006-10-02 07:40:53 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Keywords = {Gr{\"o}bner Bases},
	Mrclass = {13B25 (06F15 32B05)},
	Mrnumber = {MR826583 (87e:13006)},
	Mrreviewer = {David C. Lantz},
	Pages = {513--517},
	Publisher = {Springer},
	Series = {Lecture Notes in Comput. Sci.},
	Title = {Term orderings on the polynomial ring},
	Volume = {204},
	Year = {1985}}

@article{BuhlerReichstein2005Symmetric-funct,
	Author = {Buhler, J. and Reichstein, Z.},
	Coden = {TAMTAM},
	Date-Added = {2006-10-02 07:31:24 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Fjournal = {Transactions of the American Mathematical Society},
	Issn = {0002-9947},
	Journal = {Trans. Amer. Math. Soc.},
	Keywords = {SAGBI Bases},
	Mrclass = {82D25 (05E05 13A50)},
	Mrnumber = {MR2140442},
	Mrreviewer = {Robert James Shank},
	Number = {6},
	Pages = {2353--2377 (electronic)},
	Title = {Symmetric functions and the phase problem in crystallography},
	Volume = {357},
	Year = {2005}}

@article{Kaveh2005SAGBI-bases-and,
	Author = {Kaveh, Kiumars},
	Date-Added = {2006-10-02 07:31:24 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Fjournal = {The Michigan Mathematical Journal},
	Issn = {0026-2285},
	Journal = {Michigan Math. J.},
	Keywords = {SAGBI Bases},
	Mrclass = {14M25 (13P10 52B20)},
	Mrnumber = {MR2125537 (2006b:14091)},
	Mrreviewer = {Ivan Soprunov},
	Number = {1},
	Pages = {109--121},
	Title = {S{AGBI} bases and degeneration of spherical varieties to toric varieties},
	Volume = {53},
	Year = {2005},
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@article{Reichstein2003SAGBI-bases-in-,
	Author = {Reichstein, Zinovy},
	Coden = {COMHAX},
	Date-Added = {2006-10-02 07:28:46 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Fjournal = {Commentarii Mathematici Helvetici},
	Issn = {0010-2571},
	Journal = {Comment. Math. Helv.},
	Keywords = {SAGBI Bases; Invariant Theory},
	Mrclass = {13A50 (13P10 20C10 52B20 52B55)},
	Mrnumber = {MR1966757 (2004c:13005)},
	Mrreviewer = {Robert James Shank},
	Number = {1},
	Pages = {185--202},
	Title = {S{AGBI} bases in rings of multiplicative invariants},
	Volume = {78},
	Year = {2003},
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@article{BilleraThomasWilligenburg2006Decomposable-co,
	Author = {Billera, Louis J. and Thomas, Hugh and van Willigenburg, Stephanie},
	Coden = {ADMTA4},
	Date-Added = {2006-10-02 07:22:33 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Fjournal = {Advances in Mathematics},
	Issn = {0001-8708},
	Journal = {Adv. Math.},
	Mrclass = {05E05},
	Mrnumber = {MR2233132},
	Number = {1},
	Pages = {204--240},
	Title = {Decomposable compositions, symmetric quasisymmetric functions and equality of ribbon {S}chur functions},
	Volume = {204},
	Year = {2006},
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@article{HeubachMansour2003Counting-Rises-,
	Author = {Silvia Heubach and Toufik Mansour},
	Date-Added = {2006-10-01 15:58:38 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Title = {Counting Rises, Levels, and drops in compositions},
	Year = {2003},
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@article{Schoen2000A-note-on-the-n,
	Author = {Tomasz Schoen},
	Date-Added = {2006-10-01 15:56:54 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Journal = {The Electronic Journal of Combinatorics},
	Title = {A note on the number of ($k$,$l$)-sum-free sets},
	Volume = {7},
	Year = {2000},
	Bdsk-File-1 = {YnBsaXN0MDDUAQIDBAUGCQpYJHZlcnNpb25UJHRvcFkkYXJjaGl2ZXJYJG9iamVjdHMSAAGGoNE
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@booklet{BurrisSankappanavar1981A-Course-in-Uni,
	Author = {Stanley Burris and H. P. Sankappanavar},
	Date-Added = {2006-10-01 15:25:35 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Title = {A Course in Universal Algebra},
	Year = {1981},
	Bdsk-File-1 = {YnBsaXN0MDDUAQIDBAUGCQpYJHZlcnNpb25UJHRvcFkkYXJjaGl2ZXJYJG9iamVjdHMSAAGGoNE
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AAAAAxk=}}

@article{Sturmfels2000Solving-algebra,
	Author = {Bernd Sturmfels},
	Date-Added = {2006-10-01 15:23:07 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Journal = {Discrete Mathematics},
	Pages = {171-181},
	Title = {Solving algebraic equations in terms of $\mathcal{A}$-hypergeometric series},
	Volume = {210},
	Year = {2000},
	Bdsk-File-1 = {YnBsaXN0MDDUAQIDBAUGCQpYJHZlcnNpb25UJHRvcFkkYXJjaGl2ZXJYJG9iamVjdHMSAAGGoNE
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@misc{GoldinTeissierResolving-Singu,
	Annote = {This has something to do with toric deformations and SAGBI bases.},
	Author = {Rebecca Goldin and Bernard Teissier},
	Date-Added = {2006-10-01 13:18:26 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Keywords = {SAGBI Bases},
	Title = {Resolving Singularities of Plane Analytic Branches with One Toric Morphism},
	Bdsk-File-1 = {YnBsaXN0MDDUAQIDBAUGCQpYJHZlcnNpb25UJHRvcFkkYXJjaGl2ZXJYJG9iamVjdHMSAAGGoNE
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@article{StillmanTsai1999Using-SAGBI-bas,
	Annote = {SAGBI Bases},
	Author = {Michael Stillman and Harrison Tsai},
	Date-Added = {2006-10-01 13:18:26 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Journal = {Journal of Pure and Applied Algebra},
	Keywords = {SAGBI Bases; Invariant Theory},
	Pages = {283-302},
	Title = {Using {SAGBI} bases to compute invariants},
	Volume = {139},
	Year = {1999},
	Bdsk-File-1 = {YnBsaXN0MDDUAQIDBAUGCQpYJHZlcnNpb25UJHRvcFkkYXJjaGl2ZXJYJG9iamVjdHMSAAGGoNE
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@misc{Fornasiero2004Integration-on-,
	Abstract = {The thesis concerns the (class) structure No of Conway's surreal numbers. The 
main concern is the behaviour on No of some of the classical functions of real 
analysis, and a definition of integral for such functions. 
In the main texts on No, most definitions and proofs are done by transfinite 
recursion and induction on the complexity of elements. In the thesis I consider 
a general scheme of definition for functions on No, generalising those for sum, 
product and exponential. If a function has such a definition, and can live in a 
Hardy field, and satisfies some auxiliary technical conditions, one can obtain in No 
a substantial analogue of real analysis for that function. One example is the sign- 
change property, and this (applied to polynomials) gives an alternative treatment of 
the basic fact that No is real closed. I discuss the analogue for the exponential. 
Using these ideas one can define a generalisation of Riemann integration (the 
indefinite integral falling under the recursion scheme). The new integral is linear, 
monotone, and satisfies integration by parts. 
For some classical functions (e.g. polynomials) the integral yields the tradi- 
tional formulae of analysis. There are, however, anomalies for the exponential 
function. But one can show that the logarithm, defined as the inverse of the expo- 
nential, is the integral of 1/x as usual.},
	Annote = {discusses surreal numbers},
	Author = {Antongiulio Fornasiero},
	Date-Added = {2006-10-01 13:18:26 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Keywords = {Surreal Numbers},
	Title = {Integration on Surreal Numbers},
	Year = {2004},
	Bdsk-File-1 = {YnBsaXN0MDDUAQIDBAUGCQpYJHZlcnNpb25UJHRvcFkkYXJjaGl2ZXJYJG9iamVjdHMSAAGGoNE
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@article{McNamaraWilligenburgA-Combinatorial,
	Author = {Peter R. W. McNamara and Stephanie van Willigenburg},
	Date-Added = {2006-10-01 13:18:26 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Title = {A Combinatorial Classification of Skew Schur Functions},
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@article{Gatermann2003Applications-of,
	Annote = {This is a reference to demonstrate "applications" of SAGBI bases.},
	Author = {Karin Gatermann},
	Date-Added = {2006-10-01 13:18:26 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Journal = {Journal of Symbolic Computation},
	Keywords = {SAGBI Bases},
	Pages = {543-575},
	Title = {Applications of {SAGBI}-bases in dynamics},
	Volume = {35},
	Year = {2003},
	Bdsk-File-1 = {YnBsaXN0MDDUAQIDBAUGCQpYJHZlcnNpb25UJHRvcFkkYXJjaGl2ZXJYJG9iamVjdHMSAAGGoNE
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@article{Gobel2001Visualising-Pro,
	Abstract = {This note presents two examples for the visualization of finiteness 
and size properties of lexicographical comprehensive SAGBI bases for poly- 
nomial invariants of conjugates of the alternating and symmetric group in three 
variables. 
},
	Annote = {conjugate actions are discussed},
	Author = {Manfred G{\"o}bel},
	Date-Added = {2006-10-01 13:18:26 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Journal = {Applicable Algebra in Engineering, Communication and Computing},
	Keywords = {SAGBI Bases},
	Number = {429-435},
	Title = {Visualising Properties of Comprehensive {SAGBI} Bases - Two Examples},
	Volume = {12},
	Year = {2001},
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@inproceedings{Thiery2001Computing-Minim,
	Abstract = {
},
	Annote = {more SAGBI basis stuff},
	Author = {Nicolas M. Thi{\'e}ry},
	Date-Added = {2006-10-01 13:18:26 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Journal = {Discrete Mathematics and Theoretical Computer Science Proceedings},
	Keywords = {SAGBI Bases, Invariant Theory},
	Number = {315-328},
	Title = {Computing Minimal Generating Sets of Invariant Rings of Permutation Groups with {SAGBI}-{G}r{\"o}bner Basis},
	Year = {2001},
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@article{Miller2006Analogs-of-Grob,
	Author = {J. Lyn Miller},
	Date-Added = {2006-10-01 13:18:26 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Journal = {Journal of Symbolic Computation},
	Keywords = {Gr{\"o}bner Bases},
	Pages = {1-000},
	Title = {Analogs of {G}r{\"o}bner Bases in Polynomial Rings over a Ring},
	Volume = {11},
	Year = {2006},
	Bdsk-File-1 = {YnBsaXN0MDDUAQIDBAUGCQpYJHZlcnNpb25UJHRvcFkkYXJjaGl2ZXJYJG9iamVjdHMSAAGGoNE
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@article{Bravo2004Some-Facts-Abou,
	Author = {Ana Bravo},
	Date-Added = {2006-10-01 13:18:26 -0700},
	Date-Modified = {2008-08-05 13:03:54 -0700},
	Journal = {Trends in Commutative Algebra},
	Keywords = {SAGBI Bases},
	Title = {Some Facts About Canonical Subalgebra Bases},
	Volume = {51},
	Year = {2004},
	Bdsk-File-1 = {YnBsaXN0MDDUAQIDBAUGCQpYJHZlcnNpb25UJHRvcFkkYXJjaGl2ZXJYJG9iamVjdHMSAAGGoNE
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@article{TakemuraYoshidaFundamental-hol,
	Annote = {semigroup stuff,
possibly related to saturations},
	Author = {Akimuchi Takemura and Ruriko Yoshida},
	Date-Added = {2006-10-01 13:18:26 -0700},
	Date-Modified = {2008-08-05 13:03:55 -0700},
	Title = {Fundamental holes and saturation points of a commutative semigroup and their applications to contingency tables},
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@article {Cox1995The-homogeneous,
    AUTHOR = {Cox, David A.},
     TITLE = {The homogeneous coordinate ring of a toric variety},
   JOURNAL = {J. Algebraic Geom.},
  FJOURNAL = {Journal of Algebraic Geometry},
    VOLUME = {4},
      YEAR = {1995},
    NUMBER = {1},
     PAGES = {17--50},
      ISSN = {1056-3911},
   MRCLASS = {14M25},
  MRNUMBER = {MR1299003 (95i:14046)},
MRREVIEWER = {Mina Teicher},
}

@article {AbramovichKaruMatsukiWlodarczyk2002Torification-an,
    AUTHOR = {Abramovich, Dan and Karu, Kalle and Matsuki, Kenji and
              W{\l}odarczyk, Jaros{\l}aw},
     TITLE = {Torification and factorization of birational maps},
   JOURNAL = {J. Amer. Math. Soc.},
  FJOURNAL = {Journal of the American Mathematical Society},
    VOLUME = {15},
      YEAR = {2002},
    NUMBER = {3},
     PAGES = {531--572 (electronic)},
      ISSN = {0894-0347},
   MRCLASS = {14E05 (14E15 14L24)},
  MRNUMBER = {MR1896232 (2003c:14016)},
MRREVIEWER = {Alexandr V. Pukhlikov},
}

@article {LafaceVelasco2009A-survey-on-Cox,
    AUTHOR = {Laface, Antonio and Velasco, Mauricio},
     TITLE = {A survey on {C}ox rings},
   JOURNAL = {Geom. Dedicata},
  FJOURNAL = {Geometriae Dedicata},
    VOLUME = {139},
      YEAR = {2009},
     PAGES = {269--287},
      ISSN = {0046-5755},
     CODEN = {GEMDAT},
   MRCLASS = {14C20 (14E30)},
  MRNUMBER = {MR2481851},
       DOI = {10.1007/s10711-008-9329-y},
       URL = {http://dx.doi.org/10.1007/s10711-008-9329-y},
}


@article {Wlodarczyk1997Decomposition-o,
    AUTHOR = {W{\l}odarczyk, Jaros{\l}aw},
     TITLE = {Decomposition of birational toric maps in blow-ups \&
              blow-downs},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {349},
      YEAR = {1997},
    NUMBER = {1},
     PAGES = {373--411},
      ISSN = {0002-9947},
     CODEN = {TAMTAM},
   MRCLASS = {14E05 (14M25)},
  MRNUMBER = {MR1370654 (97d:14021)},
MRREVIEWER = {Mark Gross},
}

@article {KemperMattig2000Generic-polynom,
    AUTHOR = {Kemper, Gregor and Mattig, Elena},
     TITLE = {Generic polynomials with few parameters},
      NOTE = {Algorithmic methods in Galois theory},
   JOURNAL = {J. Symbolic Comput.},
  FJOURNAL = {Journal of Symbolic Computation},
    VOLUME = {30},
      YEAR = {2000},
    NUMBER = {6},
     PAGES = {843--857},
      ISSN = {0747-7171},
   MRCLASS = {12F12},
  MRNUMBER = {MR1800681 (2001h:12006)},
MRREVIEWER = {Jaime-Luis Garcia-Roig}
}

@unpublished{BrosnanReichsteinVistoli2007Essential-dimen,
	Author = {Patrick Brosnan and Zinovy Reichstein and Angelo Vistoli},
	Date-Modified = {2009-08-19 19:57:52 -0700},
	Note = {arXiv:math/0701903v1},
	Title = {Essential dimension and algebraic stacks},
	Year = {2007}
}

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